Yes, Cannon Soldier can tribute itself for its effect. An important thing to note is that you can do this even when Skill Drain is on the field, because Cannon Soldier's effect would resolve when it hits the graveyard.
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The only time you can ever tribute something you do not control, is if a card specifically says so. Lava Golem lets you tribute the opponent's monsters, and Soul Exchange can let you do so too. However if there is no text like this, then the tribute must come from amongst monsters you control.
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